[1]} have shown indeed that in the exponential regime this DRO predictor should be preferred to any other predictor which does not explicitely depend on data size \(T\) . We generalize this result and show that in fact it should be preferred to any other regular predictor. The key component of the proofs establishing this claim is the large deviation property of our the empirical distribution \(\hat{\mathbb {P}}_T\)  which we review in Appendix  for completeness.
